Singularity

If I play Singularity and my opponent counters it, can I still play Jhin, Meticulous Killer for [C] this turn?

You can. Jhin checks the energy spent to play a spell, not whether that spell resolved. If the energy was spent and the spell became a Finalized Chain Item (and was not undone, for example as part of step 5 of the process of play) then it doesn't matter if the spell is later countered. The energy wasn't unspent, even if the spell was countered.

359.3.e.8. If an instruction has more than one Target and fewer than all of the Targets become Invalid or Unavailable by the time the spell begins resolving, the instruction will execute, with only the Targets available and valid being operated on. Example: Singularity reads "deal 6 to each of up to two units." The instruction will execute even if one of those units is made unavailable before the spell begins.

715.2. If the Deal action has multiple targets, the amount of Damage dealt to each target is increased by Bonus Damage individually and separately. Example: Singularity is a spell that says "Deal 6 to each of up to two units." A player plays Singularity while they also control Annie, Fiery, a unit that says "Your spells and abilities deal 1 Bonus Damage." Singularity deals 1 Bonus Damage to both of its targets, dealing 7 to each.